8准晶弹性边值问题的解析解——复分析 上面的介绍让我们认识到Fourier分析非常基本,非常重要,但是计算往往非常复杂;对裂纹问题,需要求解对偶积分方程,并不是所有这类积分方程都能得到精确分析解的;同时对若干问题,例如缺口问题和其他几何上复杂的问题,Fourier分析无效,而必须借助于其他方法,其中复分析,是一种极其有效的方法.
This paper gives a brief presentation of the development on mathematical theory of elasticity of quasicrystals and some relevant topics, in which the physical framework of elasticity is discussed first, the measurement data of material constants for quasicrystals in solid phase are one of the most important basis to the theory and applications and are listed in detail. As the fundamental points, analytic methods and exact solutions for various boundary value or boundary-initial value problems are summarized, in which Chinese researchers have made significant contributions. Apart from elasticity, dynamics and plasticity of novel materials are also discussed. At last the paper offers a simple description on a possible theoretical treatment, from the view point of elasticity and hydrodynamics, to quasicrystals in soft matter phase observed very recently.